I was in a similar situation when I moved here and was waiting for closing on my house (about a month in a hotel with two dogs and a pregnant wife). Although not directly in Huntington, I stayed in two different locations:
Cross Lanes West Virginia hotels, Comfort Inn hotel close to Charleston Civic Center, Cross Lanes WV 25313
Find Cheap Hotels & Motels, Discount Hotels & Hotel Deals | Online Hotel Reservations | Red Roof Inn -- (304) 757-6394
Comfort Inn in Cross Lanes -- 30 minute commute to Huntington
Reed Roof in Teays Valley -- 20 minute commute to Huntington
The Comfort Inn is a pretty nice hotel, but weren't very friendly to the pets. Because the dogs barked when housecleaning knocked on the door, I was told that I either needed to muzzle the dogs or be present with them at all times because, "we can't have dogs barking and disturbing other guests." Which makes sense, but I didn't appreciate the manner in which they conveyed this message. Also, I think that they were a little intimidated because of the size of one of my dogs (but he is completely harmless).
I found the Red Roof Inn in Teays Valley. Don't be fooled, this is not at all a quality hotel (more of a motel). Nonetheless, I will say that (a) it was relatively clean, (b) they were very accommodating to the pets, and (c) the extended stay rate was extremely inexpensive.
Good luck...